A194606 Least k >= 0 such that prime(n)*2^k - 1 or prime(n)*2^k + 1 is prime, or -1 if no such value exists, where prime(n) denotes the n-th prime number.

0, 0, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 4, 1, 5, 3, 2, 2, 2, 1, 1, 1, 1, 3, 3, 3, 6, 1, 2, 1, 2, 1, 3, 4, 1, 2, 4, 1, 1, 3, 1, 2, 2, 1, 1, 3, 2, 1, 1, 1, 11, 1, 4, 2, 3, 1, 2, 1, 11, 1, 1, 9, 3, 6, 1, 1, 3, 3, 4, 1, 1, 2, 1, 2, 11, 4, 3, 2, 1, 4, 1, 2, 1, 1

Offset: 1

Author

Arkadiusz Wesolowski, Aug 30 2011

Keywords

• sign

Comments

A194607 gives the record values.

Examples

			For n=4, 7*2^0-1 and 7*2^0+1 are composite, but 7*2^1-1=13 is prime, so a(4)=1.
		

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Brier Number

Crossrefs

Cf. A194591, A194600, A194603, A194607, A194608, A194635, A194636, A194637, A194638, A194639.

Cf. A040081, A040076, A076335, A180247.

Programs

Mathematica

Table[p = Prime[n]; k = 0; While[! PrimeQ[p*2^k - 1] && ! PrimeQ[p*2^k + 1], k++]; k, {n, 100}] (* Arkadiusz Wesolowski, Sep 04 2011 *)